Apparatus and method for optimizing useful sunlight reflected into a room

ABSTRACT

A comprehensive method, and apparatus implementing the method, for providing beam daylighting to a room by one or more reflectors positioned in a window wall of the room. The method involves a mathematical analysis of solar and reflected beam vectors and in determining the optimum orientation of a vector normal to the reflecting surface to provide the best combination of depth of penetration of light into the room while keeping glare to an acceptable level. Arrays of both stationary and moveable reflectors implementing the method are disclosed. In the case of stationary arrays, preferably two are provided in each installation which respectively optimize performance of reflections during periods when the solar beam vector is on the easterly ana westerly sides of a line perpendicular to the window wall. All reflectors are positioned with the vector normal thereto oriented with three nonzero components in a rectangular coordinate system related to the plane of the window wall and taking into consideration the site latitude.

BACKGROUND OF THE INVENTION

The present invention relates to apparatus for installation in anopening in a building wall or roof for the purpose of enhancing interiorillumination by reflected sunlight, and to methods of determining theoptimum orientation of reflectors to achieve maximum depth ofpenetration of reflected light into the area to be illuminated withacceptably low glare. In general terms, the invention relates toimprovements in the technology commonly known as "beam daylighting."

Since the invention of the light bulb ana common availability ofelectrical power, most buildings have been designed under the assumptionthat electricity will supply interior illumination by way of lightingfixtures, and that it is unnecessary to rely upon natural light for mostor all illumination purposes. Over the more recent past, this assumptionhas been challenged on several grounds. First, artificial lightingdoesn't meet the needs of most visual tasks as well as does the broaderspectral distribution of natural sunlight. Also, the luminous efficacyof natural light (around 113 lumens/watt) is substantially higher thanthat of all commonly-used luminaries (over twice that of fluorescentsand eight times incandescents). In consequence, using natural light tomeet illumination needs in buildings not only supplants electricity thatwould otherwise be used to power artificial light fixtures, but alsolowers air conditioning loads. Thus, given good daylighting designs, theuse of natural light is highly advantageous for a number of reasons.

As used herein, and generally in the field of interest, the term "beamdaylighting" denotes the use of one or more light-reflecting surfaceswhich redirect the path of sunlight entering an enclosed area for visualor other illumination purposes. Among the prior art beam daylightingdesigns are those exemplified by U.S. Pat. Nos. 4,509,825, 4,630,8920,4,634,222, 4,699,467 and 4,989,952. Some of the previously devisedsystems employ stationary reflectors, while others include means formoving the reflecting surfaces to track solar position. Planar,parabolic, and other configurations of reflecting surfaces have beenused in beam daylighting applications, as have systems involvingreflection of incoming light from two or more surfaces in distributingthe light at the desired location. In any case, the reflecting surfaceshave a longitudinal axis which, in all known prior art systems, isoriented either horizontally or vertically. As will be shown, optimumperformance can be achieved only when the longitudinal axis of a singlereflecting surface is oriented somewhere between horizontal andvertical. This is true whether the reflectors are fixedly installed,with their orientation providing optimized performance averaged over theperiod between successive solstices, or are movable to maintainoptimized performance over a range of varying solar positions.

While it is generally recognized that orientation of the reflectingsurface(s) should provide adequate lighting in all portions of the areato be illuminated (hereafter referred to for convenience as the room),prior art daylighting systems fail to adequately consider both thespatial and the temporal aspects of reflector orientation. That is,reflector performance must take into consideration both the distance oflight penetration into the room and the level of glare in the areailluminated. Other design features, such as the relative cost,suitability for incorporation into existing structures, aestheticappearance of the installed system, maintenance requirements, etc., arealso often severely compromised or ignored.

Objects of the present invention are:

to provide a novel and improved beam daylighting system which fully orpartially replaces artificial light with natural light at an acceptablylow glare level;

to provide a method of determining optimal orientation of reflectingsurfaces at a given site location to maximize distance of penetration ofreflected light into a room (e.g., up to 30 feet) while eliminating orminimizing glare;

to provide beam daylighting structure wherein stationary reflectingsurfaces are oriented to optimize room illumination at a given latitudewhen positioned in a wall or roof opening facing in a predeterminedcompass direction;

to provide a daylighting system which is easy to maintain, suitable forinstallation in both new and existing buildings, and compatible with avariety of residential, commercial, institutional and industrialenvironments;

to provide a highly effective daylighting system which, in a firstembodiment, has no moving parts, is completely passive and functionswithout user interaction; and

to provide a daylighting system which, in a second embodiment, includesnovel structural and operational components which reorient the reflectorsurfaces during periods when they receive direct sunlight to optimizethe effectiveness of the system in terms of sending the reflected lightin a desired direction.

Other objects will in part be obvious and will in part appearhereinafter.

SUMMARY OF THE INVENTION

In accordance with the foregoing objects, the invention contemplates amathematical analysis of the solar-related orientation of alight-reflecting surface within a rectangular coordinate system, takinginto account the latitude of the site and the facing compass directionof the wall opening wherein the reflector is mounted. One aspect of theinvention is concerned with a unique method for mutually relating solarposition, reflector orientation, physical orientation of a buildingspace and direction of reflected light within the space. Directionalproperties of solar reflections are quantified within a coordinatesystem which relates the direction of the incoming and reflected beamsto the orientation of the reflector with respect to three mutuallyperpendicular axes, one of which is fixed and predetermined by thecompass direction in which building opening wherein the reflector ismounted faces. The ref lector has a longitudinal axis which, as dictatedby the method of optimizing reflector performance, is never orientedhorizontally or vertically, in contrast to prior art reflectororientations.

The method is implemented in a first embodiment by a reflectorpositioned in an opening such as a window or skylight which receivesdirect sunlight during at least a portion of the daylight hours. Atleast one such reflector is positioned to reflect light to the portionof the room farthest from the reflector and, in the usual installation,additional ref lectors will be positioned to distribute the light toother areas of the room. For convenience of construction, as well as toprovide a number of other desirable features, the reflectors arepreferably positioned with all of their longitudinal axes in a singleplane between two parallel, transparent panes.

Preferably, each window or other opening equipped with reflectorsincludes at least one positioned for optimal reflection in the desiredmanner while receiving direct sunlight when the sun is on one side of aline perpendicular to the window surface, and at least one otherpositioned for optimal reflection while receiving direct rays with thesun on the other side of such line. These are termed the ante-elevationand post-elevation sides of the window wall.

In a first embodiment, the reflectors are fixedly positioned andoriented to provide the best performance averaged over the periodbetween successive solstices. In a second embodiment, the reflectors aremovable about each of two perpendicular axes to change orientation withchanges in solar position. In each case, optimum reflector orientationis established according to the method of the invention, performance ofthe reflectors being defined and optimized in terms of both spatial andtemporal components.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of the coordinate system and unit vectors forspecifying specular reflection of sunlight;

FIG. 2 is a diagram showing the physical orientation and azimuth angleconventions (floor plan) of a room used as an example in explaining themethod of the invention;

FIGS. 3 and 4 are graphs showing optional performance function values ofstationary reflectors at site locations at several north latitudesduring ante-elevation and post-elevation periods (as such terms aredefined later herein), respectively;

FIG. 5 is a perspective view of a portion of a building wall havingwindow openings equipped with a first embodiment of the daylightingsystem of the invention;

FIG. 6 is a perspective view of a window of the type shown in FIG. 5,incorporating an array of stationary reflectors;

FIG. 7 is a perspective view, as in FIG. 5, illustrating a secondembodiment of the invention; and

FIG. 8 is a partly diagrammatic, perspective view of a series of windowsof the type shown in FIG. 7, incorporating arrays of movable reflectors.

DETAILED DESCRIPTION

The present invention may be best understood in the context of certainconventions and rules which relate the direction of a solar beam to theorientation of a reflecting surface and thus to the direction of thereflected beam. Useful examples of such conventions and rules are foundin Solar Engineering of Thermal Processes by Duffie & Beckman, JohnWiley & Sons, 1980, and "Recommended Practice for the Calculation ofDaylight Availability", by DiLaura, Journal of the IlluminatingEngineering Society, July, 1984 (pp. 381-392). The rules for specularreflection are imposed on a set of unit vectors having their tails atthe origin of a three-dimensional coordinate system. In accordance withconventional practise, letters representing vector quantities areprinted in bold type. The rules relevant to the present discussion, withreference to the coordinate system and vectors of FIG. 1, are: 1. theangle between n and r is the same as the angle between n and s, and 2.the vectors s, n and r all occur in the same plane. Vectors s and r arethe central lines of rays or "pencils" of incident and reflected light,respectively, at the specular surface whose normal is n.

In the coordinate system of FIG. 1, the x-y plane is horizontal with theaxes pointing in the four major compass directions, +x and -x pointingnorth and south, and +y and -y east and west, respectively. The +z and-z axes extend vertically upward and downward, respectively. Azimuthangles are measured from 0 to 360 degrees, clockwise from the +x axis,and zenith angles are measured clockwise from the +z axis. The unitvector labelled s represents the instantaneous position of the sun withrespect to the origin of the coordinate system. The azimuth angle (as)and zenith angle (zs) of the vector s are indicated in FIG. 1, theazimuth angle being the angle between the x axis and the projection of sin the xy plane.

The direction of a unit vector can be specified by direction cosinevalues within the coordinate system. For the unit vector s, for example,direction is specified as:

    s=sx i+sy j+sx k                                           (1)

The direction cosine values can be expressed in terms of a vector'szenith and azimuth angles, which for the example of the vector s are:

    sx=sin (zs) cos (as)                                       (2a)

    sy=sin (zs) sin (as)                                       (2b)

    sz=cos (zs)                                                (2c)

Analogous expressions apply to the vectors n and r. In the case ofstationary reflectors, only the vectors s and r have direction cosinevalues that are time-dependent. The time-varying components of the solarvector can be derived from the standard equations for the position ofthe sun (DiLaura, supra), and are:

    sx=D+E cos (w)                                             (3a)

    sy=C sin (w)                                               (3b)

    sz=A-B cos (w)                                             (3c)

where:

    A=sin (1) sin (d)                                          (4)

    B=cos (1) cos (d)                                          (5)

    C=cos (d)                                                  (6)

    D=cos (1) sin (d)                                          (7)

    E=sin (1) cos (d)                                          (8)

The variable 1 in Equations (4), (5), (7) and (8) is site latitude. Thevariable d in Equations (4)-(8) is the declination and is computed asfollows:

    d=0.4093 sin [((2π) (J-81)/368)]                        (9)

where J is the Julian day of the year. Thus, the values of A through Ewill be constant for a given day of the year at a given site. Thevariable w in Equations (3a)-(3c) is the hour angle and is defined as:##EQU1## Solar time t in Equation (10) ranges from 0 hours to 24 hours.

The time-varying components of the vector r are functions of thecomponents of s and n and must be computed explicitly. A method forcalculating the components of r may be derived from the previouslystated rules for specular reflection. The quantative formulationsrepresented by Equations (1) through (10) are familiar to those in thedaylighting field. The original work which follows results from applyingthe two general rules stated above in the coordinate system of FIG. 1.

As an example of implementing the rules for specular reflection in thecoordinate frame of FIG. 1, assume that the components of s and of n arespecified, and the problem is one of computing the components of r.Denoting the angle between s and n as A, the following three equationsmay be written using the vector dot product.

    n·r=nx rx+ny ry+nz rz=cos (A)                     (11)

    s·r=sx rx+sy ry+sz rz=cos (2A)                    (12)

    V·r=Vx rx+Vy ry+Vz rz=0                           (13)

The vector V in Equation (13) is perpendicular to the plane thatcontains s, n and r and has components (Vx, Vy, Vz), which by definitioncan be found from the vector cross product having n as one of its terms.Vector V can be computed from the cross product of vectors s and n:

    V=s×n                                                (14)

The value of cos(A) in Equation (11) can be computed directly from thedot product of s and n. The value of cos (2A) in Equation (13) can thenbe found by using a trigonometric identity. From the given information,the only unknowns in equations (11)-(13) are (rx, ry, rz), and thesecomponents of the reflection vector may be found from simultaneoussolution of the three equations. Note that this method may also be usedto find the components of any one vector if the components of the othertwo vectors are given. The solutions to the relevant equations givenabove may be accomplished in closed form, by iterative search or byother approximation methods.

Based on the definitions and equations derived above, the followingthree steps will yield the components of the unit vector r that pointsin the direction of reflected sunlight:

step 1. specify the solar position with equations (8) through (10).

step 2. state the vector components of n in the coordinate systemrepresented in FIG. 1.

step 3. solve the following system of equations for r:

    n·r=cos (A)

    s·r=cos (2A)

    V·r=0

(from Equation (14), V=s×n)

The components of the unit vector normal to a reflecting surface whichwill give a desired direction of reflected light may also be found fromthe definitions and equations derived above. The following three stepswill yield the components of the unit vector n normal to the properlyoriented reflecting surface.

step 1. specify the solar position with equations (8) through (10).

step 2. state the vector components of r (the desired direction ofreflection) in the coordinate system represented in FIG. 1.

step 3. solve the following system of equations for n:

    s·n=cos (A)

    r·n=cos (A)

    U·n=0

where U=s×r

One of the principal problems with designing beam daylighting systemsfrom stationary reflecting surfaces has been the lack of a way to ratethe performance of a given orientation of reflector. The theory derivedabove makes it possible to define a performance rating f or a reflector. In general, good performance is associated with the farpenetration of reflected light into a room with little or no glare fromthe reflections at any time of the year. There is a trade-off betweengood light penetration into a room and glare. The present inventionquantitatively defines performance rating for stationary reflectors thattakes into account both light penetration and glare.

Assume a reflecting surface, or an array of reflectors, positioned in anopening (window) above usual eye level in a wall of a room in thenorthern hemisphere. The best possible zenith angle for reflections is90° (i.e., the vector of the reflected beam is horizontal) because thisallows the reflected beam to penetrate to the back walls of the room(assuming no obstructions) without striking the ceiling and withoutglaring down onto the occupants of the room.

The best azimuth angle for reflections can be expressed in terms of theconventions introduced in the floor-plan drawing of FIG. 2. First, thefloor plan of the room is seen to occur in the xy plane of thecoordinate system of FIG. 1. Second, the window wall faces a particulardirection of the compass; the window wall in FIG. 2 happens to facesoutheast. Third, the perpendicular to the window wall is a direction inthe coordinate system that has a specific azimuth angle. The azimuthangle made by the perpendicular to the window wall is termed the room'selevation azimuth angle, and is labelled EAA in FIG. 2.

In the present nomenclature of the daylighting field, the elevationazimuth angle is the angle in the horizontal plane (the earth's surface)made by the intersection of the horizontal plane with a planeperpendicular to a window (DiLaura supra). Elevation azimuth angle canassume a value from 0 to 360 degrees in the coordinate system and is agood way to express the compass direction towards which a window faces.

Returning to the performance of a reflector, it can be seen from FIG. 2that one would want a reflected beam to enter the room in the directionof the perpendicular to the window wall. In other words, far penetrationof the reflected light occurs when the azimuth angle of reflectionequals the elevation azimuth angle of the windows. This constitutes goodperformance on the part of the reflector. Conversely, poor performancewould be associated with reflections that shine along the margins of thewindow walls and with reflections that shine back outside the room.

In summary, the best performance of a reflector is one that gives areflection having a zenith angle of 90° and an azimuth angle equal tothe elevation azimuth angle of a room. This of course is an idealsituation and never will be realized for any prolonged periods withstationary reflectors. It is possible, however, to quantify how closethe reflections from a given orientation of reflector come to the idealcondition. This is the basis for defining a performance function for areflector, and the present invention is concerned with optimizing thatperformance function.

There is one additional set of conventions that facilitates thedefinition of performance, relative to solar position and the directionin which the room f aces. In FIG. 2, two angular ranges are indicated atthe outside face of the window wall, one on each side of theperpendicular to the window wall. In the case of a planar wall, theseangular ranges will be equal, 90° angles. Between the more easterly halfof the window wall and the perpendicular to the window wall, theazimuthal positions of the sun can be said to be on the ante-elevationside of the window wall. Similarly, the azimuthal positions of the sunbetween the more westerly window wall and the perpendicular to thewindow wall can be said to be on the post-elevation side of the windowwall. If the room happens to face due south, the ante-elevation andpost-elevation azimuthal positions of the sun become the ante-meridian(a.m.) and post-meridian (p.m.) positions, respectively.

The distinction between ante- and post-elevation positions of the sunare important for the following reasons. First, no sunlight enters aroom for daylighting purposes when the sun is behind the face of thewindow wall. This is useful for defining the working time of a givenreflector on a given day of the year; the ante-elevation working time isthat period between the appearance of the sun around the more easterlyside of the window wall and the appearance of the sun at the room'selevation azimuth angle. Likewise, the post-elevation working time isthat period between the appearance of the sun at the room's elevationazimuth angle and its disappearance around the more westerly side of thewindow wall. Second, it has been found that longer total periods of beamdaylighting result when at least two stationary reflectors are providedfor a given window, one optimized for the ante-elevation sunlight andthe other for the post-elevation sunlight.

The final qualitative consideration for defining performance of areflector is that of the direction of reflection relative to thedirection of sunlight. Stationary reflectors cannot continuously providelight along the direction of the perpendicular to the window wall. Overthe course of a day, the reflections will either tend toward the samedirection as the sunlight or they will tend towards those areas of aroom that are distant f rom direct sunlight. In the former case, notmuch is accomplished, because the direct sunlight is illuminating theportion of the room into which it goes. In the latter case, thereflected light will tend to balance out the light levels with respectto what the direct sunlight provides.

Based on the consideration of general direction of reflected light, thefollowing rules can be assigned for defining good performance of astationary reflector:

(1) Reflections of ante-elevation sunlight perform well if on averagethey are towards the more easterly side of the room.

(2) Reflections of post-elevation sunlight perform well if on averagethey are towards the more westerly side of the room.

A precise expression for performance of a stationary reflector can bemade in the form of a performance function having two components, onespatial and the other temporal. The spatial component of the performancefunction is related to the azimuth angle of reflection (vector r) at atime when the reflection's zenith angle achieves 90°. The temporalcomponent is related to the duration of time that the reflections on agiven day result in glare. A high value of performance function thusoccurs for far penetration of reflected light at such a time of day thatrelatively little glare ensues. Optimal performance can be defined asthat orientation of reflector that maximizes the performance function.If performance is to be assessed for the period of an entire year, thenthe performance function must be computed for each day and averaged overthe term between successive solstices, since solar position isessentially symmetrical between solstices.

In order to derive the expressions for key components of the performancefunction, it is necessary to know when (if ever) the reflections from agiven orientation of reflector will result in glare in the areareceiving beam daylighting on a given day of the year. It is alsonecessary to know when on a given day of the year the solar positionclears the face of the window wall and when it aligns with the elevationazimuth angle of a room. From the latter, the working time available fora stationary reflector on a given day of the year can be found.

The foregoing basic concepts may be applied to calculate the time atwhich reflections begin to glare down into a room from a givenorientation of reflector. In fact, the predicted directions ofreflections from arrays having orientations useful for beam daylightingtend to follow a given pattern. When the sun is near the edge of awindow wall of a room, the reflections project upwards and close to thewindows. As the sun nears the elevation azimuth of a room, thereflections project downward and deeply into the interior of a room.This temporal pattern of reflections holds for both ante- andpost-elevation arrays.

For reflectors oriented to provide the type of beam daylighting underconsideration, it is thus possible to predict and observe that thetransition point at which the reflected beam starts to glare down intothe room is the time at which the reflections are parallel to the floor.When the reflected light is parallel to the floor, the zenith angle ofreflection is 90°. The component of r along the k direction vanishes atthat time (viz. Equation (2c)). Taken together with the fact that ingeneral, because all three vectors are coplanar,

    s×n=r×n                                        (15)

Equation (15) holds true if and only if the direction cosines of thevector on the left side are identical to the direction cosines of thevector on the right side. When the zenith of reflection achieves 90°, weobtain:

    nz sy-ny sz=nz ry                                          (16)

    nx sz-nz sx=-nz rx                                         (17)

    ny sx-nx sy=ny rx-nx ry                                    (18)

Vector r remains a unit vector when its zenith angle achieves 90°, sothat the sum of the squares of its components equals unity; this factmay be combined with the results of squaring both sides of Equations(16) and (17) and upon adding the results we obtain after somesimplification:

    (2 nx nz) sx+(2 ny nz) sy+(2 nz.sup.2 -1)sz=0              (19)

The quantities sx, sy and sz may be substituted for those given inEquations (3a) , (3b) and (3c) respectively, to give an equation of theform Equation (20). If we specify latitude, Julian day of year and theorientation of the reflector in question, the only unknowns left inEquation (20) are trigonometric functions of hour angle, w:

    L1 cos (w)=L2 sin (w)+L3                                   (20)

where

    L1=B (2 nz.sup.2 -1)-2 E nx nz                             (21)

    L2=2 C ny nz                                               (22)

    L3=2 D nx nz-A (1-2 nz.sup.2)                              (23)

Equations (21)-(23) contain the constants A, B, C, D and E (fromEquations (4)-(8) for a given day and latitude) as well as thecomponents of the vector n. Upon squaring both sides of thetranscendental Equation (20) and simplifying, the following quadraticformula is obtained:

    G1 X.sup.2 +G2 X+G3=0                                      (24)

where

    G1=L1.sup.2 +L2.sup.2                                      (25)

    G2=2 L2 L3                                                 (26)

    G3=L3.sup.2 -L1.sup.2                                      (27)

    X=sin (w)                                                  (28)

Taking the inverse sine of the appropriate root of Equation (24) givesthe hour angle at which the reflected light has a zenith angle of 90degrees. The solar hour corresponding to this condition may be found byusing Equation (10). Note that if reflections do not attain a zenithangle of 90° on a given day for a given orientation of reflector,Equation (24) will have no real roots.

If conditions are such that Equation (24) does have real roots, thenreflection zenith angle achieves 90° on the jth Julian day at a solartime to be called T_(G) (j). This is a solar time that will be useful indefining the glare component of the performance function. CombiningEquations (28) and (10) we obtain: ##EQU2##

Using very similar analytical strategies, the solar hour at which thesun achieves a specific azimuth angle, as, can be found. From thepublished functions of solar trajectory (DiLaura supra), therelationship between as and the components of the vector s can be foundfrom Equations (2a) and (2b): ##EQU3## Working through thesubstitutions, the following original equation can be derived:

    γ1 X.sup.2 +γ.sup.2 X+γ.sup.3 X=0        (31)

where

    γ.sup.1 =C.sup.2 +[E tan (as)].sup.2                 (32a)

    γ.sup.2 =2 D E tan (as)                              (32b)

    γ.sup.3 =[D tan (as)].sup.2 -C.sup.2                 (32c)

    X=cos (w)                                                  (32d)

Taking the inverse cosine of the appropriate root of Equation (31) willgive the hour angle at which the solar azimuth angle achieves a value of(as) on a given day of the year at a given latitude. This is useful forpredicting when the sun appears at the face of a room's window wall andat a room's elevation azimuth angle. The difference between those twotimes on a given day of the year defines the working time available fora daylighting array.

The constraints of specular reflection can be used in the framework of acoordinate system to solve a number of problems involving time-dependentvectors in three dimensions. The system of equations that result fromthis analysis form the basis for defining and optimizing what is termedthe performance function for stationary reflectors.

The performance function is comprised of a temporal component and aspatial component. Each of the two components is quantified for bothante-elevation and post-elevation periods, making formal use of theconventions and derivations given above.

In order to quantify the temporal component, it is necessary to definethe sun's position at four distinct times. The following notations(based on FIG. 2) are used to describe the times on the jth Julian dayof the year when, at a given latitude, the sun's positions are asfollows:

T_(EA-90) (j) solar time when solar azimuth angle is aligned with theeasterly edge of the room's window wall, i.e., when the solar azimuthangle is equal to the room's elevation azimuth angle less ninetydegrees.

T_(EA) (j)=solar time when solar azimuth angle is equal to the room'selevation azimuth angle.

T_(EA+90) (j)=solar time when solar azimuth angle is aligned with thewesterly edge of the room's window wall, i.e., when the solar azimuthangle is equal to the room's elevation azimuth angle plus ninetydegrees.

T_(G) (j)=solar time at which glare begins (as previously stated andgiven by Equation (29)).

The temporal component of the performance function, which is concernedwith the glare factor and therefore represented by the notation G(j),##EQU4## Similarly, for post-elevation cases, ##EQU5##

Note that the numerators in the nonzero portions on the right sides ofEquations (33a) and (33b) are the times between when sunlight firstbecomes available and when glare begins, on the jth Julian day of year.The denominators in Equations (33a) and (33b) are simply the workingtimes available to the reflectors on the jth Julian day of the year. Inboth cases, the nonzero temporal component of the performance functionis the fraction of the working time that reflections do not result inglare. In both cases of reflectors useful for daylighting, the zenithangle of reflection is smaller when the sun is near the edge of thewindow wall than it is when the sun is at the room's elevation azimuthangle. The temporal component thus penalizes glare that starts earlyduring the working time for a given case of reflector. It is boundedbetween 0 and 1.

The spatial component is a function of the azimuth angle of thereflected beam (vector r) at the time when its zenith angle is 90°,i.e., at solar time T_(G) (j) In FIG. 2, r' represents the projection ofvector r on the x-y plane at time T_(G) (j) on a day when thisprojection lies on the ante-elevation side of the window wall. Theante-elevation side of the window wall is located at a position given bythe room's elevation azimuth angle minus ninety degrees. The anglebetween r' and the ante-elevation side of the window wall, i.e., theazimuth angle of vector r with respect to the plane of theante-elevation side of the window wall, is denoted r_(a). Likewise, theprojection of r on the x-y plane at time T_(G) (j) on a day when theprojection lies on the post-elevation side of the window wall isrepresented by r". The post-elevation side of the window wall is locatedat a position given by the room's elevation azimuth angle plus ninetydegrees. The azimuth angle of r with respect to the plane of thepost-elevation side of the window wall at time T_(G) (j) is denotedr_(p).

The spatial component is quantified during periods when r is on theante-elevation side of the room at time T_(G) (j) as the differencebetween the room's elevation azimuth angle (EAA) less 90° and r_(a) onthe jth Julian day when r is on the post-elevation side of the room artime T_(G) (j), the spatial component is quantified as the differencebetween r_(p) on the jth Julian day and the room's elevation azimuthangle plus 90°. The spatial component is associated with penetration oflight into the room and is therefore represented by the notations P (j)(ante) and P (j) (post) for ante- and post-elevation periods,respectively. Thus, on the jth Julian day: ##EQU6##

The maximum values of Equations (34a) and (34b) occur on the jth day ofyear only if the reflections happen to point into the room along a lineperpendicular to the window wall at time T_(G) (j), i.e., if thereflected light goes straight into the room towards the back wall. Thisis the ideal case of performance and cannot be expected from a fixedreflector for more than a few days in a year. If the reflected lightachieves a zenith angle of 90° on the jth day of year but the azimuth ofreflection exceeds the limits dictated in Equations (34a) and (34b) ,the result is penalized most heavily. The spatial component is boundedbetween 0 and 1.

The performance function itself is taken as the product of the temporaland spatial components, averaged over the number of days betweensuccessive solstices (because the trajectory of the sun is symmetricalwith respect to the two half-year periods) . Actually, it is notnecessary to calculate the ante- and post-elevation values of G(j) andP(j) for every day between solstices, since a very close approximationis achieved by performing the calculations for each of a number ofequally spaced days throughout the solstice. Thus, the performancefactor C may be determined separately for ante- and post-elevationperiods as follows: ##EQU7## where N_(j) is the number of days for whichcalculations of G(j) and P(j) are performed.

From an examination of the series of equations set forth in thepreceding discussion, it will be found that values of G(j) and P(j) ,and thus of C, may be calculated if site latitude, room elevationazimuth angle and solar position at any given time on each day areknown, and vector n is specifically defined with respect to anestablished rectangular coordinate system. The net performance of thereflector is thus quantified for each of a number of days and averagedover a term between successive solstices. Determining the maximum valueof C, i.e., optimizing the performance function, is thus an iterativeprocess, involving repeated solution of equations 35(a) and 35(b) (andall necessary preceding equations) with a series of different vectors nuntil the particular vector is found which maximizes C. The process is,of course, expedited by use of a properly programmed digital computer.The actual optimization procedure selected to solve Equations (35a) and(35b) is not as important as the result from the optimization.

Representative values of optimal performance are plotted as functions ofroom elevation azimuth angles for a number of latitudes in the U.S., inFIGS. 3 and 4, shows optimal performances for ante- and post-elevationcases, respectively. A very good approximation to optimal orientation ofreflector for a given latitude and room elevation azimuth angle can bemade for room elevation angles between 130° and 230°. The approximationis based on the azimuth angle of reflector (an) and on the zenith angleof reflector (zn). The components of the vector n are then given by:

    nx=sin (zn) cos (an)                                       (36a)

    ny=sin (zn) sin (an)                                       (36b)

    nz=cos (zn)                                                (36c)

Values of n which maximize C in Equations (35a) and (35b) weredetermined for a number of site latitudes as well as for a number ofroom elevation azimuth angles. The azimuth and zenith angles of thevector n that gave optimal performance for these cases weresystematically examined. Zenith angles of the optimal n vectors showedalmost no dependence on site latitude, only on room elevation azimuthangle. The azimuth angles of the optimal n vectors had a morecomplicated dependence on both room elevation azimuth angle and sitelatitude.

Customary fitting procedures were applied for the plots of optimalazimuth angle of vector n as a function of room elevation azimuth angle.The types of curve fits included linear, logarithmic, exponential andpower functions. Of these, the power function fits consistently gaveexcellent correlation coefficients (>0.95) for those portions of theplots that are of interest here. The optimal value of reflector azimuthangle (an) for a given room's elevation azimuth angle (EAA) is wellapproximated by:

    an=a (EAA).sup.b                                           (37)

The values of a and b are given for ante-elevation cases in Table 1, andfor post-elevation cases in Table 2. Retain all significant figures whenperforming calculations with values from Tables 1 and 2. For latitudesthat are not listed in Tables 1 and 2, excellent approximations areprovided by linear interpolations for the values of the constants. Theoptimal value of the zenith angle of vector n as a function of roomelevation azimuth angle can be found from linear interpolation fromTable 3.

The approximations do not hold so well for room elevation azimuth anglesless than about 130° and greater than about 230°. For these cases,Equations (35a) and (35b) should be optimized directly.

                  TABLE 1                                                         ______________________________________                                        Coefficients for Approximation Formula                                        for Optimal Azimuth Angle of stationary                                       Reflectors, at Various U.s. Latitudes.                                        Ante-Elevation Cases.                                                         Latitude,                                                                     Degrees        Coefficients                                                   North          a        b                                                     ______________________________________                                        20             0.0004074                                                                              2.2872384                                             25             0.0002352                                                                              2.4043733                                             30             0.0006175                                                                              2.2242912                                             35             0.0012011                                                                              2.1056092                                             40             0.0021152                                                                              2.0099800                                             45             0.0019976                                                                              2.0305734                                             50             0.0023313                                                                              2.0073444                                             ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        Coefficients for Approximation Formula                                        for Optimal Azimuth Angle of stationary                                       Reflectors, at Various U.s. Latitudes.                                        Post-Elevation Cases.                                                         Latitude,                                                                     Degrees        Coefficients                                                   North          a        b                                                     ______________________________________                                        20             17.182430                                                                              0.5508543                                             25             11.441473                                                                              0.6258393                                             30             13.829961                                                                              0.5889940                                             35             19.497210                                                                              0.5200871                                             40             16.702357                                                                              0.5471227                                             45             11.732292                                                                              0.6126464                                             50             12.563902                                                                              0.5969792                                             ______________________________________                                    

                  TABLE 3                                                         ______________________________________                                        Optimal Zenith Angles of stationary Reflectors,                               at Various Room Elevation Azimuth Angles,                                     for the U.s.                                                                  Room Elevation                                                                Azimuth Angle Ante-Elevation                                                                            Post-Elevation                                      (deg)         Cases       Cases                                               ______________________________________                                         90           X.sup.1     39.8°                                        135           44.7°                                                                              42.3°                                        180           42.9°                                                                              42.9°                                        225           42.3°                                                                              44.7°                                        270           39.8°                                                                              X.sup.2                                             ______________________________________                                         .sup.1 For elevation azimuths between 90 and 135 degrees, use zenith angl     = 44.7° for anteelevation cases.                                       .sup.2 For elevation azimuths between 225 and 270 degrees, use zenith         angle = 44.7° for postelevation cases.                            

The foregoing discussion has demonstrated how the surface normal vectorof a reflecting surface may be oriented to maximize performance ofreflections in terms of both temporal and spatial components. Thispermits design of a beam daylighting system with a single, optimallyoriented reflector, or a plurality of like-oriented reflectors. Such asystem assumes, of course, that maximum penetration of the reflectedbeam into the room represents the ideal situation, i.e., optimizedperformance, in terms of the spatial component. In many applications itwill be desirable to provide, in addition to the ref lector (s) havingthe previously defined optimal orientation, one or more additionalreflectors. While such additional reflectors will be, by definition,sub-optimal, they may nevertheless be useful for purposes such asproviding a more uniform distribution of light throughout the room,concentrating additional light in one or more specific target areas,avoiding direct beams in some locations, etc.

FIGS. 5 and 6 illustrate a simplified version of a window wallfenestration system and a window construction used therein incorporatingan array of differently oriented reflectors. Wall 10 is an external wallof the room which receives beam daylighting, facing in a known compassdirection at a known site latitude and provided with appropriateopenings wherein the windows are mounted. The illustrative system ofFIG. 5 includes a plurality of side-by-side windows, each having threevertically stacked sections. Lower and middle sections 12 and 14,respectively, are conventional, transparent paned windows of anysuitable design with no reflecting elements. Upper sections 16 arewindow constructions according to the present invention.

An example of one of sections 16 is shown in more detail in FIG. 6. Thesurrounding frame is of square or rectangular configuration, includingupper and lower portions 18 and 20, respectively, and side portions 22and 24. The frame portions may be of any suitable construction such aswood or the roll-formed aluminum now common in the insulating glassindustry. The frame of section 16 is divided into right and leftsections, generally denoted by reference numerals 26 and 28,respectively, by mullion 30.

A first plurality of reflectors 32 are fixedly supported within rightsection 26 of the frame, and a second plurality of reflectors 34 arefixedly supported in left section 28. Each of reflectors 32 and 34 is,in the illustrated embodiment, of rectangular configuration, having aplanar reflecting surface and extending along a longitudinal axisbetween opposite ends respectively supported by mullion 30 and one ofthe frame members. The particular means employed for supporting the endsof reflectors 32 and 34 is of no consequence in the present invention,although the orientation of each reflector within the frame,, andconsequently with respect to wall 10 and the direction in which itfaces, is determined in accordance with the invention. All of reflectors32 and 34, as well as mullion 30, are positioned between transparentpanes 36 and 38, in or parallel to the parallel planes of the front andrear (or outwardly and inwardly facing) sides of the surrounding frame.

In the window construction of FIG. 5, reflectors 32 are orientated tobest suit the beam daylighting requirements of the room duringante-elevation periods of solar position; likewise, reflectors 34 areoriented to provide the best beam daylighting during post-elevationperiods of solar position. Thus, at least one of reflectors 32 ispositioned with the vector n normal to its reflecting surface orientedto maximize the value of C in equation (35a). Likewise, at least one ofreflectors 34 is positioned with its vector n oriented to maximize C inequation (35b). The orientations of remaining (sub-optimal) reflectorswill depend to some extent upon the desired characteristics of lightdistribution in the room being illuminated, while ensuring that anyglare resulting from the reflections is not so great as to interferewith visual tasks to be performed in the room. It may be noted that theorientations of reflectors 34 will be symmetrical with those ofreflectors 32 only when the window wall faces directly south.

It is assumed that the beam daylighting system is intended to provideillumination for performance of a particular visual task, or generaltype of task, and that the physical parameters of the room and anycontents thereof which will have an effect on performance of daylightingare known. For example, the presence of physical obstructions mayrequire the redirection of beams which have been reflected into the roomby reflectors 32 and 34. Also, reflections should not be directed uponother visual working surfaces within the room which require directviewing for performance of the visual task, e.g., blackboards or othersuch working surfaces. Therefore, it is preferred in many applicationsthat sunlight be reflected into the room along beam paths higher thanboth the maximum eye height of individuals performing visual taskswithin the room and of any working surfaces.

Although considerations governing the orientation of the plurality ofreflectors in an array will-vary from one installation to another, anexample of a procedure which may be used to determine severalorientations of reflectors for an array useful for many circumstanceswill be given. One observation useful in designing arrays is that theextremes of glare from an optimal reflector orientation occur when thesun is at the room's elevation azimuth angle on the day of the wintersolstice. The key consideration in designing an array is to keep anyglare from the reflections below a certain acceptable level throughoutthe year. Of course, even the optimal reflector orientation is notaltogether glare-free, but represents the best trade-off between glareand depth of penetration of light. Thus, the following seven-stepprocedure may be used to obtain the orientations of four suboptimalreflectors in an array:

1. Determine the optimal reflector orientation according to thepreviously provided information. The vector normal to the surface of theoptimally oriented reflector is designated n_(o).

2. Determine the zenith angle of the sun when it is at the room'selevation azimuth angle on the day of the winter solstice. The vectorrepresenting solar position at this time with respect to the reflectoris designated s_(o).

3. Determine the azimuth and zenith angles of the reflection of s_(o)from n_(o), which are denoted a_(o) and z_(o), respectively.

4. For the same s_(o), determine the orientation of reflector that givesa reflection with an azimuth angle of a_(o) and a zenith angle ofreflection of (z_(o) -10°). The vector normal to the surface of thisreflector is designated n₁.

5. Repeat Step 4, except now find the orientation of reflector thatgives a zenith angle of reflection of (z_(o) -20°). The vector normal tothe surface of this reflector is designated n₂.

6. Repeat Step 4, except now find the orientation of reflector thatgives a zenith angle of reflection of (z_(o) -30°). The vector normal tothe surface of this reflector is designated n₃.

7. Repeat Step 4, except now find the orientation of reflector thatgives a zenith angle of reflection of (z_(o) -40°). The vector normal tothe surface of this reflector is designated n₄.

This procedure produces a set of four orientations of sub-optimalreflectors. Simulations show that the sub-optimal orientations obtainedaccording to this procedure never result in glare throughout the year.Other types of simulations show that there is an increasing spread ofazimuth angles of reflections from the four orientations that becomesmost pronounced on the day of the summer solstice. The seven steps canspecify the orientations for an array of either ante- or post-elevationazimuth applications.

Not all four of the designed orientations need to be implemented in anarray. The number of orientations deemed suitable for a givenapplication will depend on other factors such as size of the window.Precedence should be given to the optimal orientation of reflector.Also, there must be enough open space in the array not to block outdiffuse daylight on overcast days. Only one or two orientations seem tobe necessary for windows that face nearly due east or west, especiallyin northern latitudes where the average working time available forillumination throughout the year is relatively brief for those compassdirections. For rooms that face southeast and southwest, there may beenough of a disparity in orientations between the ante- andpost-elevation azimuth halves of a window such that one or more of thefour options is rejected to get as close as possible to a visual matchof patterns of reflections.

The foregoing discussion has provided a method of determiningorientations of stationary reflectors in terms of their surface normalvectors both for reflectors which optimize performance of reflectionsand for those which are sub-optimal by definition but useful infulfilling overall beam daylighting objectives. In order to be easilyincorporated in existing fenestration systems, the reflectors arepreferably incorporated in a window construction such as that of FIG. 6which, in turn, is mounted in a window wall such as that of FIG. 5. Insuch systems, all reflectors of each window construction havelongitudinal axes lying in a single plane, parallel to the plane of thewindow wall.

The reflectors are positioned to achieve the desired orientation oftheir surface normal vector by rotation about two axes, oneperpendicular to the window wall and the other its own longitudinalaxis. In customary terminology, these would be considered the pitch androll axes, respectively, of the reflector with respect to the windowwall. No rotation about the vertical (yaw) axis is performed fororientation purposes since the reflector must remain with itslongitudinal axis in a fixed plane parallel to the window wall. Thefollowing discussion will be useful in calculating the pitch and rollangles which will provide the desired orientation of surface normalvectors for reflectors having a known, non-adjustable, yaw angle.

In order to conveniently compute these angles for a given orientation ofreflector, the vector n can be multiplied by an appropriatetransformation matrix that is a function of window orientation.

Specifically, define an angle ρ_(z) of room orientation in the x-y plane(from FIG. 2) where the "z" subscript denotes rotation about the z-axis,such that:

    ρ.sub.z =Window Elevation Azimuth Angle-180°    (38)

The appropriate transformation matrix is then |R_(z) | and is defined tobe: ##EQU8##

A transformed version of n can be defined as n' and can be found bymultiplying n by |R_(z) |:

    n'=n |R.sub.z |                          (40)

The components of n' are then given by:

    n'=nx' i'+ny' j'+nz' k'                                    (41)

Note that the coordinate system of the support frame itself, relative tothe system shown in FIG. 2, is given by the rectangular notation {i',j', k'}. This is equivalent to a rectangular system rotated by an angleρ_(z) about the z-axis relative to the system shown in FIG. 2; thus, thedirection k' is equivalent to the direction k in the original system.

In terms of the components of n', the pitch and roll angles may becomputed as follows. ##EQU9##

Note that the sign conventions for the descriptive angles of ante- andpost-elevation azimuth arrays are defined by the convention of Equation(38).

It will be seen that the pitch and roll angles of a strip of reflectorintroduce a compound angle where one edge of the reflector intersectsthe inner edge of the support frame. The strip of reflector intersectsan edge of the frame at a slope related to the components of n'.Specifically, the line of intersection of a strip of reflector having asurface normal n' can be found from the vector cross product of n' withthe unit vector perpendicular to the inner edge of the frame.

The lines of intersection that n' makes with each of the inner frameedges are:

    n' x (-j')=nz' i'-nx' k'                                   (44)

    n' x (-k')=-ny' i'+nx' j'                                  (45)

    n' x (j')=-nz' i'+nx' k'                                   (46)

    n' x (k')=ny' i'-nx' j'                                    (47)

It is interesting to note that if the slope of the line of intersectionat the right and left inner edges of the frame is taken to be the changein the z' direction divided by the change in the x' direction; then,from Equations (44) and (47): ##EQU10##

This is one way to derive the expression of roll angle given in Equation(43). The pitch angle can be found from the cross product of n' with i'.

The beam daylighting systems and computational methods disclosed up tothis point have been directed to reflectors which are fixedly mounted. Asecond embodiment of the invention is concerned with reflectors whichare rotatable about their pitch and roll axes to maintain the directionof reflected beams substantially fixed as solar position changes. Windowwall 40 of FIG. 7 includes a fenestration system similar to that of FIG.5, having lower and middle sections 42 and 44 comprising conventional,transparent-paned windows. Upper sections 46 comprise windowconstructions incorporating arrays of planar reflectors mounted incylindrical- surrounding frames.

Three horizontally adjacent sections 46 are shown in FIG. 8, eachcomprising a plurality of reflectors 48 supported within surroundingframe 50 of cylindrical configuration. Each frame 50 is rotatablymounted in a suitable opening in window wall 40, thereby providingcollective pitch axis rotation of all reflectors 48 supported withineach frame 50. Reflectors 48 are of the same type as reflectors 32 and34, i.e., rectangular strips having a longitudinal axis and a planarreflecting surface. Reflectors 48 are supported at opposite ends withineach of frames 50 for rotation about the respective longitudinal axes ofthe reflectors; i.e., each of reflectors 48 is rotatable about its rollaxis.

Although the present invention is not particularly concerned with theparticular means used to rotate the frames and reflectors, a somewhatdiagrammatic example is provided in FIG. 8. A portion of the outerperiphery of each frame 50 is provided with gear teeth 52 and the outputshaft of electrical servomotor 54 is connected to gear 56, which isengaged with teeth 52 of one of frames 50. Each of frames 50 may beindependently rotatable by separate motor, or two or more frames 50 maybe mutually engaged by one or more gears 58, as illustrated, to impartrotation from one to one or more others of frames 50.

Similarly, means are provided for rotating reflectors 48 about theirrespective roll axes either individually or collectively. In theillustrated embodiment, servomotors 60 are mounted upon each of frames50, and each motor 60 is suitably engaged with one of reflectors 48within the frame on which the motor is mounted. All reflectors 48 withina given frame 50 may be connected to one another for simultaneousrotation about their respective longitudinal (roll) axes, e.g., in thenature of conventional Venetian blinds. Also, all reflectors 40 within agiven frame 50 may be rotated by equal amounts in response to rotationimparted to one reflector, or a desired amount of unequal rotation maybe imparted by, for example, suitable gearing arrangements.

The object of using movable reflectors will, in most cases, be tomaintain the distribution of reflected light within the room in asubstantially constant pattern throughout times that beam daylighting isprovided. Thus, in order to direct reflected beams to a specific targetarea, a reflector must be rotated to change the orientation of itssurface normal vector as the relative solar position changes throughouteach day. That is, using previous conventions, in order to maintainvector r substantially constant, vector n must be reoriented to conformto changes in vector s. With a window wall facing in a known compassdirection at a known site latitude, the time-dependent orientation ofvector n and the changes in pitch and roll angles of reflectors having aknown yaw angle may be determined in accordance with the previousdiscussion.

It is preferred that the electrical signals to which motors 54 and 60are responsive be controlled by preprogrammed instructions from acomputer such as the schematically indicated CPU-based controller 62.Controller 62 may be programmed by conventional techniques, utilizingthe information set forth herein. However, a thoroughly reliable andintervention-free system of control may be achieved with artificialintelligence techniques within the current state of the art. Suchtechniques involve the use of so-called neural networks capable ofadaptively handling many parameters at once to accomplish a goal and aredescribed, for example, in "A Universal Optimization Network" by Harth,et al, Proceedings of the Special Symposium on Maturing Technologies andEmerging Horizons in Biomedical Engineering, IEEE (pp. 87-89, 1988).

Programming pad 64, solar beam sensing array 66 and directional locatinglaser gear 68 are connected to the CPU in order to initialize thesystem. Rough estimates of site latitude, solar time and compassdirection of the window wall, together with the date, are entered intothe CPU by means of programming pad 64. The locating laser indicates thedesired direction of the reflected beam during routine operation. Sensorarray 66 is placed next to locating laser 68 at the desired targetlocation for verification of the direction and intensity of reflectedlight. The neural network then starts to refine the rough estimatespreviously entered as it "trains" over the course of one sunny day,throughout which the neural network causes the reflectors to project thebeam toward sensor array 66. Optimal operation of the neural network isdetermined by optimal illumination of sensor array 66 under sunnyconditions. When performance of the neural network is satisfactory, theend of initialization is signaled. The system is then ready to provideyears of intervention-free illumination of the target area. Of course,various reflectors or arrays may be directed to different target areas,in which case separate initialization is performed for each area.

Although natural light is preferable to artificial light for a number ofreasons in addition to energy conservation, as previously pointed out,it is nevertheless desirable that energy consumed in moving an array ofreflectors be less than the energy saved by supplanting artificial withnatural light. To this end, particular attention should be given tooptimizing efficiency of the mounting and actuating elements in beamdaylighting systems employing movable reflectors. Power can be suppliedfrom batteries charged by solar-tracking photovoltaic cells and/orstandard 110 VAC. Specialized control systems ensure minimum power ofmotion; theoretical development of such control is presented in"Physical Principles For Economies of Skilled Movements" by W. L.Nelson, Biological Cybernetics 46 135-147 (1983).

From the foregoing, it will be seen that the present invention providesbeam daylighting systems and window constructions utilized therein whichare much more efficient in terms of illuminating a room, or selectedareas thereof, than prior art systems of this class. The inventionencompasses both stationary and movable reflectors, and arrays thereof.With regard to stationary reflector arrays, the invention furtherprovides a novel and very useful method of optimizing performance ofreflections for beam daylighting purposes.

What is claimed is:
 1. Apparatus for providing beam day-lighting to aroom having an exterior envelope a portion of which faces in a compassdirection to receive direct sunlight for at least a period during eachday of at least a portion of the year, said apparatus comprising:a) amember having a light-reflecting surface; b) means defining an openingin said portion of said envelope; and c) means supporting said member insaid opening in an orientation wherein all directional components of avector normal to said surface have values other than zero in all ofthree mutually perpendicular coordinate directions, of which one isperpendicular to the plane of said opening and the other two are in theplane of said opening.
 2. The apparatus of claim 1 wherein substantiallyall of said reflecting surface is planar.
 3. The apparatus of claim 1wherein said supporting means fixedly positions said member in saidopening.
 4. The apparatus of claim 1 wherein said member has alongitudinal axis in said plane of said opening.
 5. The apparatus ofclaim 4 wherein said opening is in a substantially vertical plane andsaid longitudinal axis is oriented in other than either horizontal orvertical.
 6. Apparatus for providing beam day-lighting for illuminationof an area wherein one or more individuals are positioned at apredetermined maximum eye height to perform visual tasks involvingdirect viewing of a working surface, said area being located in anenclosed space having an exterior envelope a portion of which faces in apredetermined compass direction at a predetermined site latitude, saidenvelope having surf ace portions surrounding an opening, said apparatuscomprising:a) at least one opaque member having a highly specular,light-reflecting surface; and b) means supporting said member in saidopening with said reflecting surface in a position to receive directsunlight for at least a period during each day of at least a portion ofthe year, and to reflect said sunlight not more than once into saidenclosed space along beam paths which optimize performance ofreflections in terms of both temporal and spatial components averagedover the period between successive solstices at locations in saidenclosed space higher than that of both said maximum eye height and saidworking surface.
 7. The apparatus of claim 6 wherein at least apredetermined portion of said light-reflecting surface is planar and alldirectional components of a vector normal to said predetermined portionhave values other than zero in all of three mutually perpendicularcoordinate directions, a first of which is perpendicular to the plane ofsaid opening and the second and third of which are in the plane of saidopening.
 8. The apparatus of claim 6 wherein said opaque member has alongitudinal axis in the plane of said opening.
 9. The apparatus ofclaim 8 wherein said supporting means fixedly position said member insaid opening in an orientation wherein said longitudinal axis is otherthan either horizontal or vertical.
 10. The apparatus of claim 9 whereinat least a first and a second opaque member are fixedly supported insaid opening, each of said members having a longitudinal axis in theplane of said opening.
 11. The apparatus of claim 10 wherein said firstand second opaque members are oriented to optimize said performance ofreflections during ante-elevation and post-elevation periods,respectively.
 12. The apparatus of claim 11 and further including firstand second pluralities of opaque members each having a light-reflectingsurface, said first and second pluralities respectively including saidfirst and second members, all of said members having a longitudinal axisin the plane of said opening and oriented other than either horizontallyor vertically.
 13. A beam daylighting system for a room having a windowwall facing in a predetermined compass direction at a known latitudeproviding direct sunlight to said window wall on at least some daysduring both ante-elevation and post-elevation periods when solarposition is on easterly and westerly sides, respectively, of a lineperpendicular to said window wall, said system comprising, incombination:a) first and second opaque members, each having a highlyspecular surface; b) first support means fixedly positioning said firstmember in an opening in said window wall to receive direct sunlight onsaid surface and reflect said sunlight not more than once into said roomalong beam paths which optimize performance of reflections in terms ofboth temporal and spatial components averaged over the period betweensuccessive solstices during said ante-elevation periods; and c) secondsupport means fixedly positioning said second member in an opening insaid window wall to receive direct sunlight on said surface and reflectsaid sunlight not more than once into said room along beam paths whichoptimize performance of reflections in terms of both temporal andspatial components averaged over the period between successive solsticesduring said post-elevation periods.
 14. The beam daylighting system ofclaim 13 wherein said specular surface of each of said opaque members issubstantially planar.
 15. The beam daylighting system of claim 14wherein each of said first and second members has a longitudinal axis inthe plane of said opening.
 16. The beam daylighting system of claim 15wherein each of said first and second members extend between oppositeends and are fixedly supported by said first and second support means,respectively, at each of said ends.
 17. The beam daylighting system ofclaim 16 wherein said first and second support means each includeportions of a rectangular frame.
 18. The beam daylighting system ofclaim 17 wherein said first and second members are supported inlaterally spaced positions within said frame.
 19. The beam daylightingsystem of claim 18 wherein said first and second support meansrespectively comprise first and second substantially rectangular framesmounted in side-by-side relation in said opening.
 20. The beamdaylighting system of claim 19 wherein said frames each have front andrear sides respectively bounded by first and second, parallel planes,said first and second members being positioned entirely between saidfirst and second planes.
 21. The beam daylighting system of claim 20 andfurther including a pair of transparent panes closing said front andrear sides of said frames on opposite sides of said first and secondmembers.
 22. A window construction for installation in an opening in anexterior wall facing in a predetermined compass direction at a knownlatitude to provide beam daylighting to a room bounded on one side bysaid exterior wall, said window construction comprising:a) a surroundingframe structure having front and rear sides bounded by parallel, firstand second planes; b) first and second opaque members each having alongitudinal axis extending between first and second ends and a highlyspecular surface; and c) means supporting said members within saidsurrounding frame structure with said longitudinal axis of each of saidmembers in a third plane between and parallel to said first and secondplanes, and with said specular surfaces of said first and second membersrespectively oriented to optimize performance of reflections of sunlightinto said room in terms of both temporal and spatial components duringante-elevation and post-elevation periods of solar position with respectto a line perpendicular to said parallel planes when said framestructure with said first and second members supported therein isinstalled in said opening.
 23. The window construction of claim 22 andfurther including a pair of transparent panes supported upon said framestructure in planes substantially parallel to said first and secondplanes and on opposite sides of said first and second members.
 24. Thewindow construction of claim 22 wherein said frame structure defines asubstantially rectangular, enclosed area.
 25. The window construction ofclaim 22 wherein said frame structure defines a substantially circular,enclosed area.
 26. The window construction of claim 22 and furtherincluding a mullion extending across and dividing said frame structureinto first and second portions wherein said first and second members arerespectively supported.
 27. The window construction of claim 26 whereinsaid mullion forms a part of said supporting means.
 28. A method ofoptimizing the performance of reflections of direct sunlight into a roomfor beam daylighting purposes from a reflecting surface of a membersupported in a planar opening in an exterior wall of said room, saidmethod comprising:a) defining a rectangular coordinate system havingfirst, second and third mutually perpendicular axes, said first andsecond axes lying in a horizontal plane and being perpendicular andparallel, respectively, to the plane of said opening, and said thirdaxis being vertical; b) determining the geographic latitude of saidroom, and the compass direction in which said exterior wall faces,thereby defining the vector s representing solar position with respectto said member in said coordinate system at all times during each day;and c) positioning said surface with the vector n normal theretooriented with three nonzero components in said rectangular coordinatesystem and the vector r of solar beams reflected by said member intosaid room optimized in terms of both temporal and spatial components.29. The method of claim 28 wherein said positioning step includesfixedly supporting said member within said opening with vector noriented to optimize performance of reflections along vector r in termsof both temporal and spatial components averaged over the period betweensuccessive solstices.
 30. The method of claim 29 wherein said member issupported with vector n oriented to optimize said performance ofreflections during periods when vector s is on the easterly side of saidfirst axis, and including the further step of fixedly supporting asecond member in said opening with the vector n' normal to thereflecting surface of said second member oriented with three nonzerocomponents in said rectangular coordinate system and the vector r' ofsolar beams reflected by said second member into said room optimized interms of both temporal and spatial components averaged over the periodbetween successive solstices during periods when vector s is on thewesterly side of said first axis.
 31. The method of claim 28 whereinsaid member is movably supported in said opening, and including thefurther step of moving said member to vary the orientation of vector ncommensurately with changes in vector s to maintain vector rsubstantially constant throughout at least a predetermined portion of atleast some days.
 32. The method of claim 31 wherein said member has alongitudinal axis and is supported with said longitudinal axis in theplane of said opening, said step of moving said member comprisingrotating said member about at least one of said longitudinal axis and anaxis parallel to said first axis.
 33. The method of designing an arrayof reflectors each having a planar reflecting surface and a longitudinalaxis for positioning in an opening disposed in a vertical plane in anexterior wall facing in a known compass direction at a known sitelatitude to provide beam daylighting to a room partially bounded by saidwall, said method comprising:a) defining a rectangular coordinate systemhaving first, second and third mutually perpendicular axes, said firstand second axes lying in a horizontal plane and being perpendicular andparallel, respectively, to the plane of said opening, and said thirdaxis being vertical; b) determining the components within saidcoordinate system of a vector n_(o) normal to the reflecting surface ofa first reflector of said array which optimizes performance ofreflections in terms of both temporal and spatial components during oneof ante-elevation and post-elevation periods, when solar position withrespect to said opening is on easterly and westerly sides, respectively,of a line perpendicular to the plane of said opening averaged over theperiod between successive solstices; c) determining the elevationazimuth angle between compass direction north and said known compassdirection; d) determining for any day of the year at said site latitudethe solar time at which the sun is at said elevation azimuth angle; e)determining the zenith angle of the vector s_(o) representing solarposition with respect to said first reflector at the time when the sunis at said elevation azimuth angle on the day of the winter solstice; f)determining the azimuth and zenith angles, a_(o) and z_(o),respectively, of reflections of s_(o) from n_(o) ; and g) determiningthe components within said coordinate system of the components of avector n₁ normal to the reflecting surface of a second reflector of saidarray which provides reflections having an azimuth angle a_(o) and azenith angle z₁ a predetermined number of degrees smaller than z_(o) atsolar position s_(o).
 34. The method of claim 33 and including thefurther step of fixedly supporting said first and second reflectorswithin said opening with the surface normal vectors of the respectivereflecting surfaces oriented at n_(o) and n₁, respectively.
 35. Themethod of claim 34 wherein each of said first and second reflectors hasa longitudinal axis and is supported with said longitudinal axisparallel to said plane of said opening.
 36. The method of claim 33 andincluding the further step of determining the components within saidcoordinate system of vectors n₂ . . . n_(n) normal to the respectivereflecting surfaces of a plurality of additional reflectors of saidarray wherein all of said reflectors provide reflections having anazimuth angle a_(o) and successive ref lectors provide reflectionshaving respective zenith angles z₂ . . . z_(n) each of which is smallerthan that of the preceding reflector, all at solar position s_(o). 37.The method of claim 36 wherein successive ref lectors providereflections having respective zenith angles smaller than that of theimmediately preceding reflector by said predetermined number of degrees.38. The method of claim 37 and including the further step of fixedlysupporting said additional reflectors within said opening with thesurface normal vectors of the respective reflecting surfaces ofsuccessive reflectors of said array oriented at n₂ . . . n_(n),respectively.
 39. An array of reflectors mounted in a substantiallyplanar opening of an exterior wall of a room, said wall facing a knowncompass direction and said room being at a known geographic latitude, toprovide beam daylighting at a location within said room withoutsignificant glare during both ante-elevation periods, when solarposition with respect to said array is on the easterly side of a lineperpendicular to said wall, and post-elevation periods, when solarposition with respect to said array is on the westerly side of saidline, said array comprising:a) at least one first reflector having afirst longitudinal axis and first, highly specular, substantially planarreflecting surface; b) first support means fixedly supporting said firstreflector within said opening with said first longitudinal axis in aplane parallel to the plane of said opening and with said firstreflecting surface positioned with the vector normal thereto oriented toprovide optimized performance of reflections during said ante-elevationperiods in terms of both temporal and spatial components averaged overthe period between successive solstices; c) at least one secondreflector having a second longitudinal axis and a second,, highlyspecular, substantially planar reflecting surface; and d) second supportmeans fixedly supporting said second reflector within said opening withsaid second longitudinal axis in a plane parallel to the plane of saidopening and with said second reflecting surface positioned with thevector normal thereto oriented to provide optimized performance ofreflections during said post-elevation periods in terms of both temporaland spatial components averaged over the period between successivesolstices.
 40. The array of reflectors of claim 39 and further includinga first plurality of additional reflectors each having a longitudinalaxis and a respective, highly specular reflecting surface and supportedwithin said opening with said longitudinal axis of each in a planeparallel to the plane of said opening, the respective reflecting surfaceof each reflector of said first plurality being positioned with thevector normal thereto oriented to provide optimized performance ofreflections in terms of temporal components and predetermined,sub-optimized performance of reflections in terms of spatial componentsduring said ante-elevation periods averaged over the period betweensuccessive solstices.
 41. The array of reflectors of claim 40 andfurther including a second plurality of additional reflectors eachhaving a longitudinal axis and a respective, highly specular reflectingsurface and supported within said opening with said longitudinal axis ofeach in a plane parallel to the plane of said opening, the respectivereflecting surface of each reflector of said second plurality beingpositioned with the vector normal thereto oriented to provide optimizedperformance of reflections in terms of temporal components andpredetermined, sub-optimal performance of reflections in terms ofspatial components during said post-elevation periods averaged over theperiod between successive solstices.
 42. The array of reflectors ofclaim 41 and further including a surrounding frame mounted in saidopening, and said first and second support means comprising first andsecond portions, respectively, of said frame.
 43. The array ofreflectors of claim 42 wherein said frame includes front and rear sidesrespectively bounded by first and second planes parallel to the plane ofsaid opening, and all of said reflectors lie entirely between said firstand second planes.
 44. The array of reflectors of claim 43 and furtherincluding a pair of transparent panes supported within said frame onopposite sides of said reflectors, said panes respectively closing saidfront and rear sides of said frame.
 45. The array of reflectors of claim43 and further including a mullion extending across said frame anddividing the latter into said first and second portions.
 46. The arrayof reflectors of claim 45 wherein each of said reflectors extendsbetween first and second ends one of which is supported by said mullionand the other of which is supported by said frame.
 47. An array ofreflectors mounted in a substantially planar opening of an exterior wallof a room, said wall facing in a known compass direction to receivedirect sunlight for a period during each day of at least a portion ofthe year, and said room being at a known geographic latitude, to providebeam daylighting at a target area within said room, said arraycomprising:a) a frame structure surrounding a defined area; b) aplurality of reflectors each having a longitudinal axis and a highlyspecular reflecting surface; c) means supporting said ref lectors withinsaid frame for rotation about said longitudinal axis of each reflector;d) means supporting said frame structure in said opening with saiddefined area and said opening in parallel planes for rotation about afixed axis perpendicularly intersecting said defined area; and e) motivemeans for effecting rotation of said reflectors about said longitudinalaxis of each and of said frame about said fixed axis in a mannerdirecting solar beams reflected by said reflectors to illuminate saidtarget area without objectionable glare throughout changes in solarposition with respect to said reflectors.
 48. The array of reflectors ofclaim 47 wherein said frame structure is substantially cylindrical andsaid defined area is circular.
 49. The array of reflectors of claim 48wherein said longitudinal axis of each of said reflectors is in a planeparallel to said plane of said opening and parallel to said longitudinalaxis of each of the others of said reflectors.
 50. The array ofreflectors of claim 47 and further including computerized control meansfor said motive means.
 51. The array of reflectors of claim 50 whereinsaid control means includes a neural network and initializing meanspermitting said neural network to respond to actual changes in solarposition.
 52. The array of reflectors of claim 50 wherein said motivemeans includes at least first and second electrical motor means foreffecting rotation of said reflectors and said frame, respectively, eachof said motor means being responsive to signals from said control means.